Question

A machine which manufactures black polythene dustbin bags, is known to produce 3% defective bags. Following a major breakdown of the machine, extensive repair work is carried out which may result in a change in the percentage of defective bags produced. To investigate this possibility, a random sample of 200 bags is taken from the production and a count reveals 14 defective bags. What may be concluded? Run a significance test using a 0.05 α-level of significance

Answer 1

H0: p = 0.03

Ha: p 0.03

Sample proportion = 14 / 200 = 0.07

Test statistics

z = ( - p ) / sqrt [ p ( 1- p) / n ]

= ( 0.07 - 0.03) / sqrt [ 0.03 ( 1 - 0.03) / 200 ]

= 3.32

From two tailed test,

p-value = 2 * P(Z > z)

= 2 * P(Z > 3.32 )

= 2 * 0.0005

= 0.0010

Since p-value < 0.05 , Reject the null hypothesis.

We have sufficient evidence to conclude that there is change in the percentage of defective bags

produced